The generator matrix

 1  0  1  1  1  2  X  1  1  1 X+2  1  1  1 X+2  1  1 X+2  1  1  2  1  1  2  1  1  2  1  1  2  0  1  1  1 X+2  1  X  1  2  1  1 X+2  1 X+2  1  1  1  1  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  X  1  1  1  1  2  1  1  1  1  1  1  1  1  1  1  1 X+2  1
 0  1  1 X+2 X+3  1  1 X+1  X  3  1  2  X X+1  1  X X+1  1  0  1  1  0  1  1  0 X+3  1 X+2  1  1  1  2 X+3  X  1  1  1  0  1  0  X  1  X  1 X+3  3 X+3  1 X+2 X+1  3 X+3  1 X+1  3 X+1  3 X+1 X+1  1  3 X+3  3 X+3  3  0  2  2  2 X+2 X+2  X  X  X  0  2  2  X X+2 X+2  X X+1  0  2  2  1  1  1  2
 0  0  X  0 X+2  X  X  2  X  2  0  X X+2  2  0  0  X X+2  0 X+2  0 X+2  2 X+2  0  X  X  0  X X+2  0 X+2  2 X+2  0  2  X  0  0  X  0 X+2  X  0  2  2  X  X  2 X+2 X+2 X+2  X  0  2  0  2 X+2  X X+2 X+2  2  0  2  0  2  2  0  X X+2  2  0  2 X+2  X  X  2  0 X+2  X  X  2  2  0 X+2  0 X+2 X+2  X
 0  0  0  2  0  2  2  2  0  2  0  2  0  0  2  2  2  0  0  2  2  2  0  0  2  0  0  0  2  2  0  0  0  2  0  2  0  2  2  0  0  2  2  2  2  0  0  2  2  0  2  2  0  0  0  2  2  2  2  0  0  0  0  2  2  2  0  2  2  2  0  2  2  2  2  2  2  0  0  0  0  2  2  0  2  2  0  2  0
 0  0  0  0  2  2  0  0  2  2  2  2  0  2  2  2  0  0  2  2  0  0  0  2  2  0  0  2  0  0  2  2  2  2  0  2  2  0  2  0  0  2  0  0  0  0  2  2  2  0  0  2  2  0  2  2  0  0  2  0  2  0  2  2  0  0  0  2  0  2  0  0  0  0  2  0  2  2  2  2  0  2  0  2  0  0  2  0  2

generates a code of length 89 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+78x^84+84x^85+110x^86+56x^87+163x^88+128x^89+134x^90+56x^91+75x^92+28x^93+50x^94+16x^95+10x^96+16x^97+8x^98+5x^100+1x^104+2x^114+2x^116+1x^136

The gray image is a code over GF(2) with n=356, k=10 and d=168.
This code was found by Heurico 1.16 in 0.59 seconds.